Joint Ventures and Technology Adoption

Transcription

1 Jont Ventures and Technology Adopton Kazuhko Mkam School o Economcs, Unversty o Hyogo Kezo Mzuno School o Busness Admnstraton, Kwanse Gakun Unversty March 08 Abstract Ths paper examnes rms ncentves or jont ventures when they have an opportunty to adopt an ecent producton technology. When rms are heterogeneous n terms o producton ecency, an ecent rm owes a larger cost share to establsh a jont venture than an necent rm under a unanmty cost-sharng rule. Due to ths cost-sharng eect, a jont venture deters rms rom adoptng an ecent technology. Then, because o rms weak ncentve to adopt an ecent technology, a jont venture s more lkely to occur when rms have an opportunty to determne ther producton technologes endogenously. Keywords: jont ventures, technology adopton, cost-sharng eect. JEL classcaton: L43, L5, L96. We would lke to thank Yasuhro Ara, Koch Futagam, Yukhro Kdokoro, Steen Lppert, Toshhro Matsumura, Hrosh Osano, and Dusan Paredes or ther valuable comments. We also thank semnar partcpants at Koch Unversty, Nanzan Unversty, Okayama Unversty, Senan Gakun Unversty, and the Contract Theory Workshop or ther nsghtul dscussons. Ths research s supported by JSPS KAKENHI Grant # 5K0349. Correspondng author: Kezo Mzuno, School o Busness Admnstraton, Kwanse Gakun Unversty, --55 Uegahara, Nshnomya, Hyogo , Japan. Phone: E-mal: kmzuno@kwanse.ac.jp

2 Introducton Cooperaton or nvestment s consdered an eectve tool or rms n a market to enhance ther actvtes or to avod ormdable nvestment costs. For example, jont ventures or research and development (R&D) can be regarded as cooperaton or nvestment. The S-LCD Corporaton establshed by Sony and Samsung as an amorphous TFT LCD panel producton company and the global Hybrd Cooperaton among GM, Damler, Chrysler, and BMW or the development o hybrd cars are amous examples o R&D jont ventures. Smlarly, nrastructure acltes have occasonally been bult by consortums between nrastructure companes. The deployment o hgh-bandwdth subsea ber optc cables lnkng the Unted States and Japan called "Unty" and the South Fuj gas ppelne bult by Tokyo Gas, Shzuoka Gas, and Tekoku Petroleum are examples o such consortums. In ths paper, we examne rms ncentves or jont ventures and ther perormances n a smple theoretcal ramework. Although there s a large body o lterature regardng jont ventures or cooperatve nvestments, we propose a derent model by sheddng lght on the ollowng our aspects. Frst, n our model, the lkelhood o a jont venture s endogenously determned by comparng the prot under a jont venture wth that n a non-cooperatve nvestment regme. In the exstng lterature, several studes such as d Aspremont and Jacquemn (988), Kamen et al. (99), Suzumura (99), Chen and Ross (000)(003), and Ln and Sagg (00) compare the perormances between cooperatve nvestment (or a jont venture) and non-cooperatve nvestment by takng the occurrence o cooperatve nvestment as gven. In contrast, we presume that a jont venture can occur and only all member rms agree to cooperate by comparng ts prot n the two nvestment regmes. That s, the lkelhood o a jont venture s one o the man ssues o ths paper. Even n the management lterature, many studes address the phenomenon o coopetton, whchs also related to cooperatve nvestment. See Dorn et al. (06) or ts systematc lterature revew. A ew studes such as Cho (003) and Bourreau and Doğan (00) address the lkelhood o cooperatve nvestment va derent approaches than ours.

3 Second, we take a derent approach to ormulate how to establsh a jont venture rom those n the exstng lterature. Most studes, such as d Aspremont and Jacquemn, presume that n the cooperatve nvestment regme, each member rm nvests ndependently to maxmze a jont prot oallmemberrms by takng a degree o spllovers as gven. They then compare the total nvestment level n the cooperatve nvestment regme wth that n the non-cooperatve nvestment regme. By contrast, we assume that all member rms have to agree upon the sze o a aclty (.e., the level o total nvestment) and each member rm can use that aclty to produce ts own nal products. That s, a jont venture s nterpreted as producng a club (or publc) good. 3 In addton, we allow rm heterogenety n terms o producton ecency. The sze o a aclty and each rm s share o the total nvestment cost, ncludng a xed aclty cost, are then determned by heterogeneous rms under a cost-sharng rule, whch s called the unanmty cost-sharng rule. The unanmty cost-sharng rule smultaneously determnes the sze o a aclty and each rm s cost share o nvestment, the detals o whch are explaned n Secton 3. Thrd, each member rm has an opportunty to make a technology choce beore or ater the establshment o a jont venture. In act, rms may upgrade ther producton processes (.e., process nnovaton) n adjustng to a jont venture because they may want to be n a better poston to determne the detals o contract terms (e.g., how to share nvestment costs between member rms, the sze o a aclty) or the jont venture. Smlarly, rms may re-organze ther labor locatons or governance structures, whch can also be consdered a technology choce. Hence, a technologcal change, such as an organzatonal or process nnovaton, s related to rms decsons regardng the undertakng o a jont venture. Examples o the relatonshp between a jont venture and the assocated technology choce are ound n the real busness world. When Sony and Samsung jontly establshed the S-LCD Corporaton n 004, they had prevously agreed to orm a coalton or ths 3 Note that producng a club good s nterpreted as the case o ull spllovers generated rom nvetments to all member rms.

4 research jont venture by a Memorandum o Understandng on October 8, 003. Between the agreement and the establshment o S-LCD, Sony had been restructurng ts corporate governance at an approxmate cost o 33 mllon yen rom 003 to 005. A porton o ths restructurng process can be consdered a strategc use o technology choce or a jont venture. Regardng the example o the South Gas ppelne n Japan, Shzuoka Gas decsvely mplemented gas calore upgrades when the ppelne was bult. Fourth, when we consder the relatonshp between a jont venture and rms technology choces, the tmng o these two nvestment decsons matters because the decson made n the rst stage plays a role as a strategc commtment devce that can aect the other decson n the next stage. In ths paper, we analyze two scenaros wth respect to the tmngs o two knds o nvestment: a jont venture and a technology choce. The rst scenaro addresses the case n whch a rm chooses ts producton technology n antcpaton o the opportunty to undertake a jont venture wth other rms; we call ths scenaro strategc technology choce. A typcal case o a strategc technology choce s one n whch multple ncumbent rms want to undertake a jont venture n order to engage n R&D to develop a new product or to enhance ther aclty deployment. Ths s because ncumbent rms can easly make ther technology choces through the exstng producton actvtes beore they decde on whether to agree to a jont venture. The consortum or buldng the South Gas ppelne mentoned above can be consdered an example o strategc technology choce. The second scenaro addresses the case n whch rms decde whether to undertake a jont venture n antcpaton o each rm s choce o producton technology. Ths scenaro s called strategc cooperaton. Strategc cooperaton s sutable or the case n whch rms want to undertake a research jont venture to develop a new product. Accordng to the product le-cycle theory, rms rstestablshaproductnamarketandthennvestn process nnovaton to lower producton cost. 4 Moreover, jont ventures under a government 4 See Levtt (965) or the product le-cycle theory. Klepper (996) provdes emprcal evdence that supports the theory. 3

5 ntatve are consdered an example o strategc cooperaton because potental member rms can relect ther upcomng technologes n the contract terms o such jont ventures. For example, when solar power systems were developed by a jont venture n the Japanese natonal project rom 980 to 000, several member rms mplemented the organzatonal restructurng wth the establshment o a new aclty or solar power development. 5 To shed lght on the above our aspects, we buld a smple model n whch rms have an opportunty to undertake a jont venture to buld a new upstream aclty that has a demand-enhancng eect wth a xed aclty cost. In addton, rms can choose a downstream producton technology non-cooperatvely; ths aects the cost share o upstream nvestment each rm must ncur under the jont venture. The cost share o upstream nvestment s determned by a unanmty cost-sharng rule under whch nether rm dsagrees on cost sharng or on the sze o a new upstream aclty. Then, rms can choose ther downstream technology non-cooperatvely beore or ater undertakng a jont venturetobuldanewupstreamaclty. Analyzng ths model, we rst show that when rms undertake a jont venture or demand-enhancng nvestment, they have less ncentve to adopt an ecent technology than they have n a non-cooperatve nvestment regme. Ths ndng results due to the cost-sharng eect under a unanmty cost-sharng rule n a jont venture regme. Accordng to the unanmty cost-sharng rule under a jont venture, an ecent rm must ncur a larger cost share o the upstream nvestment than an necent rm when rms are heterogeneous n terms o producton ecency. Ths s because the benet generated by the nvestment s greater to an ecent rm than to an necent rm. Due to ths negatve workng o the cost-sharng eect or an ecent rm, each rm has a weak ncentve to adopt an ecent technology when they have an opportunty to choose ts own technology. In other words, although a jont venture has the advantage o avodng the duplcaton o xed costs, t also generates a negatve mpact on a rm s ncentve to adopt an ecent 5 See METI (0). 4

6 technology. To the best o our knowledge, ths paper s the rst attempt to ormally show the negatve mpact o a jont venture or cooperatve nvestment on a rm s technology choce. Second, we show that a jont venture s more lkely to occur when rmshaveanopportunty to choose ther producton technologes endogenously n the above two scenaros than n the case n whch a rm s technology s exogenously gven. In a non-cooperatve nvestment regme, each rm has the benet o spllovers rom a rval rm s nvestment, whereas t has to ncur the total cost o ts own upstream nvestment. Then, n the non-cooperatve nvestment regme, each rm has a strong ncentve to adopt an ecent technology because t can enjoy the demand-enhancng eect not only rom ts own nvestment but also rom ts rval s nvestment. However, as the magntude o the xed cost to buld an upstream aclty ncreases, each rm s ncentve to undertake a jont venture gradually ncreases due to the cost-sharng property o a jont venture. Then, when rms have an opportunty to choose ther producton technologes, they can take advantage o a jont venture n order to avod the nvestment cost or an ecent technology. These results n the two scenaros ndcate that one o the two nvestment decsons actually relates to the other and s used as a strategc devce to enhance a rm s prots. For example, n the scenaro o strategc technology choce, a rm has a tendency to use a jont venture to enjoy ts cost-sharng property wth the delay o the adopton o an ecent technology rather than buldng ts own aclty wth the adopton o an ecent technology. By contrast, n the scenaro o strategc cooperaton, a rm can strategcally use the opportunty to undertake a jont venture by ncludng the benet rom ts technology choce n the contract terms o a jont venture. In both scenaros, jont ventures have a benet to avod the duplcaton o the buldng cost o aclty rom a welare vewpont. However, as ndcated above, jont ventures also reduce a rm s ncentve to adopt an ecent technology due to the cost-sharng eect that works negatvely aganst an ecent rm. Ths s because rom a rm s perspectve, t can take 5

7 advantage o a jont venture s cost-sharng property by strategcally delayng the adopton o an ecent technology. Hence, ths s a welare-detrmental aspect o jont ventures. Many studes examne the perormance o cooperatve nvestments and jont ventures; see, or example, Katz (986), Kamen et al. (99), Suzumura (99), Cho (993), Chen and Ross (003), and Ghosh and Morta (006). The ormer our studes ocus on comparng nvestment levels between cooperatve nvestment and non-cooperatve nvestment by takng the degree o spllovers as gven. Chen and Ross (003) examne the characterstcs o strategc allances and nput jont ventures. In ther model, a xed-sze producton aclty bult by a jont venture produces nputs wth constant margnal cost. Ghosh and Morta (006) examne the relatonshp between cooperatve nvestment or product nnovaton and market competton by assumng that cooperaton or product nnovaton reduces product derentaton. All these studes examne how cooperatve behavor regardng nvestments contrbutes to socal benets by comparng cooperatve nvestment wth non-cooperatve nvestment, but the decson regardng cooperaton or nvestment s taken as gven n these studes. In addton, they nether menton the mpact o cooperatve nvestment on rms technology choces. Regardng a rm s technology choce, Mlls and Smth (996) and Elbereld (003) analyze rms ncentves to adopt an ecent technology, and they show the occurrence o endogenous rm heterogenety n olgopoles. Nether paper addresses the relatonshp between cooperaton or nvestment and rms non-cooperatve technology choces. The most relevant studes are Ln and Sagg (00) and Bourreau and Doğan (00)(07). These researchers examne a lnk between product R&D and process R&D under sequental tmng whereby product R&D by rms s ollowed by process R&D. 6 Ln and Sagg analyze whether cooperatve product R&D enhances process R&D by assumng that process nnovaton ncreases the degree o horzontal product derentaton. They take a decson on cooperaton as gven. In the settng o Bourreau and Doğan, cooperaton or product 6 Ths tmng corresponds to the scenaro o strategc cooperaton n our analyss. 6

8 nnovaton has the benet o sharng nvestment costs, whle ts dsadvantage s that t nduces erce competton by reducng the degree o horzontal product derentaton. Then, the degree o cooperaton s endogenously determned n ther model. In contrast to ther model, we assume that nvestment under a jont venture has only a demandenhancng eect. We then analyze the ssue regardng when a jont venture s lkely to occur when rmshaveanon-cooperatvechocetomprovetherproductontechnology. 7 Furthermore, we ocus on the tmng o these two decsons and ndcate the possblty o rm heterogenety that occurs endogenously n equlbrum. The remander o ths paper s structured as ollows. Secton presents the model. Secton 3 provdes a benchmark n whch rms have an opportunty to establsh a jont venture when ther technologes are exogenously gven. Secton 4 characterzes the equlbrum n the scenaro o strategc technology choce. The equlbrum n the scenaro o strategc cooperaton s examned n Secton 5. We conclude the paper wth some remarks n Secton 6. The Model To examne the relatonshp between the lkelhood o a jont venture and rms technology choces, we consder a duopoly model wth an opportunty to nvest n a new aclty wthn the context o vertcally related sectors. 8 There are two vertcally related sectors n a market: an upstream sector and a downstream sector. The two sectors are requred to supply servces to consumers n the market. Two rms, rm and rm, want to buld a new upstream aclty to upgrade the qualty o ther servces or to extend the deployment o the upstream aclty to a new regon. In other words, the nvestment or a new upstream aclty has a demand-enhancng eect 7 The lterature on group or network ormaton s related to our research n that cooperaton s endogenously determned; see, or example, Deroan and Gannon (006), Goyal (007), Goyal and Josh (003), and Jackson (008). 8 The context o vertcally related sectors s not essental or the analyss n ths paper. The context s used only to make the analyss relevant to the examples ntroduced n Secton. 7

9 on the servce. The nvestment cost to buld a new upstream aclty s represented by F (θ) = e F + (θ), where e F s a constant and (0) = 0, 0 (θ) > 0, and (θ) > 0. e F represents a xed aclty cost, whereas (θ) represents the nvestment cost or the sze θ o the upstream aclty (or the level θ o upstream nvestment). An example o the sze θ s the network capacty o moble communcatons. Note that n our model, the new upstream aclty s treated as a club or publc good among the two rms. 9 We also assume that θ relects the magntude o a demand-enhancng eect, as stated shortly. For analytcal tractablty, we use a specc ormo(θ) =kθ / to derve the explct soluton n the ollowng analyss. Here, k (> 0) represents the ecent parameter o the nvestment technology. The utlty o a representatve consumer s represented by the ollowng quadratc uncton: U (q,q,q 0 )=(V + θ)(q + q ) q +q q + q + q0, where V s the basc wllngness to pay or the servce; q ( =, ) s the quantty served by rm, 0 and q 0 s a numerare good. Here, we assume that the servces provded by the two rms are perect substtutes, and the level o upstream nvestment θ relects the magntude o the demand-enhancng eect. Then, the nverse demand uncton or good s gven by p =(V + θ) q q j, j =,, and 6= j. Snce buldng a new upstream aclty ncludes a xed cost ef, rms and are lkely to have an ncentve to own the aclty jontly to share the nvestment cost. When a new upstream aclty s ownershp s shared by rms and, the stuaton s called a jont venture regme. In the jont venture regme, the two rms cooperatvely determne the sze o the aclty, θ, and the share o the nvestment cost F (θ) that each rm must ncur 9 The ormulaton o cooperatve nvestment as a club/publc good s used also n Cabral (000) and Chen and Ross (003). 0 In broadband markets and n energy markets, such as electrcty and gas markets, the quantty may be deemed to be the number o customers served by downstream rms. 8

10 based on a cost-sharng rule. Any cost-sharng rule should satsy the ollowng equaton. s + s =, () where s ( =, ) s the share o the nvestment cost that rm (=, ) ncurs. There are several canddates or the cost-sharng rules. In our analyss, we use the unanmty cost-sharng rule. The unanmty cost-sharng rule s dened as the rule under whch no rm dsagrees regardng ts share o nvestment cost and the assocated nvestment level. In other words, under the unanmty sharng rule, each rm s prot s maxmzed by that nvestment level wth ts share o the nvestment cost. As shown n Secton 3, the man reason or us to use ths rule s that t determnes not only the level o upstream nvestment θ but also the cost share that each rm must ncur ncludng the xed cost ef. The propertes o the unanmty cost-sharng rule and the procedure or ts dervaton are explaned n Secton 3 below. In addton, each rm n our model has an opportunty to choose ts downstream producton technology. We suppose that there are two alternatve producton technologes, called new and old. The old technology s the status quo technology, whch s represented by a constant margnal cost c o. Conversely, we represent the new technology as a lower constant margnal cost c (< c o ) that s adopted by ncurrng an nvestment cost. We assume that a rm s technology choce rom these two alternatves s made noncooperatvely. Then, n the jont venture regme, the prot orm depends on ts technology choce downstream. When rm chooses the old technology (hereater called the old-technology rm), ts prot s represented by π =(p c o ) q s F (θ). When rm chooses the new technology (hereater called the new-technology rm), ts 9

11 prot s represented by π =(p c) q s F (θ). However, at least one o the rms does not agree to undertake the jont venture, each rm should nvest n the upstream aclty alone. Ths stuaton s called anoncooperatve nvestment regme. In the non-cooperatve nvestment regme, the nverse demand uncton or good s gven by p =(V + θ + βθ j ) q q j, j =,, and 6= j, where θ (θ j )srm s (rm j s) nvestment, and β ( [0, ]) represents the degree o demand spllovers. In moble communcatons, β s consdered the degree o roamng agreement between rms and. Then, n the non-cooperatve nvestment regme, rm s prot wth the old technology and that wth the new technology are respectvely represented by π =(p c o ) q F (θ ),and π =(p c) q F (θ ). Note that n the non-cooperatve nvestment regme, each rm ncurs not only the nvestment cost or the sze o ts upstream aclty θ but also the xed cost F e on ts own, whereas t can enjoy the spllovers rom the other rm s nvestment. We examne two scenaros regardng the tmng o two nvestment decsons. The rst scenaro s called strategc technology choce. In ths scenaro, we analyze the stuaton n whch a rm can use ts downstream technology choce as a strategc devce by antcpatng the opportunty to undertake a jont venture. Hence, n the rst stage, rms and choose ther downstream producton technologes non-cooperatvely by antcpatng the 0

12 opportunty or the undertakng o a jont venture n the second stage and the downstream competton n the thrd stage. Then, n the second stage, each rm determnes whether t actually agrees on the jont venture to buld a new upstream aclty. I both rms agree, the new upstream aclty s owned by them and they cooperatvely determne the sze θ and each rm s share o the nvestment cost, s and s (the jont venture regme). By contrast, at least one o the rms does not agree to undertake the jont venture, each rm should nvest n the aclty alone (the non-cooperatve nvestment regme). Then, n the thrd stage, rms and compete wth quanttes n the retal market (Cournot competton). Conversely, the second scenaro s called strategc cooperaton. In ths scenaro, n the rst stage, each o the two rms determnes whether t agrees on the jont venture by antcpatng the opportunty to choose ts own downstream technology. Here, we assume that each rm scostshareandtheszeotheupstreamacltyaredetermnedbasedon the rm s producton technology, whch s chosen n the second stage. In the second stage, rms and choose ther downstream producton technologes non-cooperatvely. Frms and compete wth quanttes n the thrd stage. We dene v V c o and c c o c. Usng these dentons, we make the ollowng assumptons or analytcal smplcty. Assumptons () v> c and () k>. Assumpton () mples that the basc wllngness to pay s sucently large that the oldtechnology rms can be actve n a market. Assumpton () allows us to restrct our ocus to the nteror solutons o rms prot-maxmzng nvestments n the ollowng analyss.

13 3 A Benchmark: The Case o Exogenous Producton Technologes In ths secton, we prepare a benchmark n whch each rm s producton technology s exogenously gven. Gven a rm s producton technology (n partcular, c o or c), we examne when the jont venture regme s lkely to occur by comparng the equlbrum n that regme wth that n the non-cooperatve nvestment regme. 3. Jont venture equlbrum Frst, we derve the equlbrum n the jont venture regme. Gven the level o upstream nvestment θ n the jont venture regme, the equlbrum Cournot producton or rm nthethrdstagesgvenby q = 3 ((V + θ) c + c j ),, j =,, 6= j, () where c {c o,c}. Then, to derve the equlbrum prots and the nvestment levels n the jont venture regme, we need to characterze the unanmty cost-sharng rule wth derent downstream technologes under the jont venture. 3.. The unanmty cost-sharng rule As mentoned n the prevous secton, under the unanmty cost-sharng rule, each rm s prot s maxmzed by the nvestment wth the assocated cost share that the rm must ncur. The procedure o the unanmty cost-sharng rule s as ollows. Suppose that a cost share s s gven to rm under the constrant o P = s =.Then,rm proposes total nvestment level θ (),whchmaxmzestsprot, ncludng the nvestment cost t ncurs. I θ () 6= θ (),aderent cost share s proposed to each o the two rms under the constrant o P = s =. Ths step s repeated untl the condton that θ () = θ () holds. When

14 θ () = θ () holds,thecostshares and the assocated nvestment level θ = θ () = θ () under the unanmty cost-sharng rule are determned. The ollowng lemma characterzes the unanmty cost-sharng rule and the nvestment level n our model speccaton. In the lemma, we also show that the unanmty costsharng rule acheves the nvestment that maxmzes the jont prots o all rms: θ = arg max θ Π P = π. Lemma Suppose that each rm s prot n the jont venture regme s hgher than that n the non-cooperatve nvestment regme. Then, n the speccaton o our model, the cost share and the assocated nvestment level under the unanmty cost-sharng rule are characterzed as ollows. s = 3(V c + c j ) k (c j c ), =,, 6= j, 3k (V (c + c )) θ = (V (c + c )). 9k 4 Then, the unanmty cost-sharng rule acheves the nvestment that maxmzes the jont prots o all rms. Proo. See Appendx A. There are three remarks that should be mentoned regardng Lemma. Frst, n the exstng studes that address the perormance o a jont venture or cooperatve nvestment n comparson wth that o non-cooperatve nvestment, a sem-colluson approach s used regardng the ormulaton o cooperatve nvestment. Speccally,nthatapproach,each member rm chooses the nvestment level t mplements to maxmze the jont prots o all member rms by takng the degree o spllovers as gven n the nvestment stage, and they compete wth each other n the producton stage. Although the benet o ths approach s that t makes t easy to compare the nvestment level accomplshed n a cooperatve See d Aspremont and Jacquemn (988), Kamen et al. (99), Suzumura (99), Ln and Sagg (00), and Foros et al. (00). 3

15 nvestment regme wth that n a non-cooperatve nvestment regme, the approach cannot address how to share a xed cost that mght be ncluded n the buldng o a aclty. In contrast, n ths paper, the establshment o a new upstream aclty s treated as a club or publc good among rms and. Under the unanmty cost-sharng rule, gven the cost share s to rm, therm proposes a sze o the aclty (a total nvestment level) θ that maxmzes ts prot. Then, the unanmty cost-sharng rule determnes not only the sze o the aclty θ but also each rm s cost share s o the total nvestment cost that ncludes the xed aclty cost. We should note that, because the establshment o the aclty s ormulated as a club or publc good, the demand-enhancng eectappearsas the degree o spllovers s ull (.e., β =). However, there s no spllover rom the socal vewpont, because the nvestment cost s totally ncurred by rms and. Second, under the unanmty cost-sharng rule, a new-technology rm, whch has a lower margnal cost than an old-technology rm, must ncur a larger cost share o the upstream nvestment than an old-technology rm. Ths ndng can be vered by s s = (c c )(9k 4) 3k (V (c + c )). Thus, s (<) s and only c (<) c. Ths s because the margnal benet generated by the upstream nvestment to a rm wth a low margnal cost (a new-technology rm) s greater than that to a rm wth a hgh margnal cost (an old-technology rm). Hence, a rm that obtans a hgher margnal benet should pay a larger share o the nvestment cost than a rm reapng a lower benet. The ndng that a new-technology rm ncurs more cost than an old-technology rm mples that the cost-sharng eect generated n the jont venture regme ders between rms when ther producton technologes are derent. In partcular, an old-technology In ths respect, the unanmty cost-sharng rule s remnscent o the Lndahl mechansm wthn the context o publc-goods provson. 4

16 rm can enjoy more benets rom the cost sharng than a new-technology rm. Furthermore, we can very that, as k becomes small, s s s becomes large s 6= s. Ths ndng ndcates that an mprovement o nvestment technology enhances the derence n the cost sharng between derent technology rms. Thrd, we should note that even we use a Nash barganng rule as an alternatve costsharng rule, t also derves the jont-prot maxmzng nvestment. However, the costsharng ormula under a Nash barganng rule s derent rom that under the unanmty cost-sharng rule. 3 Nevertheless, we can very that the qualtatve result that a newtechnology rm ncurs a larger cost share than an old-technology rm also holds under a Nash barganng rule. 3.. Prots and nvestments n the jont venture regme Usng the unanmty cost-sharng rule, we can represent the equlbrum prots and the assocated nvestment levels n the jont venture regme when takng rms downstream technologes as gven n the ollowng way. 4 () When two rms choose a new technology, rm s prot and the assocated nvestment are π cc = 9 (v + c + θ cc ) µ k (θ cc ) + ef = k (v + c) 9k 4 e F, θ cc = 4(v + c) 9k 4. () When two rms choose an old technology, rm s prot and the assocated nvestment are 3 Indeed, the cost-sharng ormula under a Nash barganng rule s more complcated than that under the unanmty cost-sharng rule. 4 In the ollowng equatons, the superscrpt "c" ("o") represents a new (old) technology. The rst (second) superscrpt represents rm s (rm j s) producton technology. 5

17 π oo = 9 (v + θ oo ) µ k (θ oo ) + ef kv = 9k 4 F e, θ oo = 4v 9k 4. () When rm chooses an old technology and rm j chooses a new technology, rm s prot and the assocated nvestment are π oc = µ 9 (v c + θ oc ) s oc k (θ oc ) + ef µ (3kv (3k ) c)(v c) 3kv (3k ) c = 3(9k 4) 3k (v + c) θ oc (v + c) =,wheres oc 3kv (3k ) c =. 9k 4 3k (v + c) ef, (v) When rm chooses a new technology and rm j chooses an old technology, rm s prot and the assocated nvestment are π co = µ 9 (v + c + θ co ) s co k (θ co ) + ef µ (3kv +(3k ) c)(v + c) 3kv +(3k ) c = 3(9k 4) 3k (v + c) θ co (v + c) = (= θ oc ),wheres co 3kv +(3k ) c =. 9k 4 3k (v + c) ef, 3. Non-cooperatve nvestment equlbrum Next, we derve the equlbrum n the non-cooperatve nvestment regme by takng rms technologes as gven. In the analyss hereater, we restrct our attenton to the case o ull spllovers (.e., β =) to compare the non-cooperatve nvestment equlbrum wth the jont venture equlbrum. The reason to ocus on the case o ull spllovers 6

18 s as ollows: As stated n secton 3.., the demand-enhancng eect works as the degree o spllovers s ull n the jont venture regme, because the upstream aclty s treated as a club/publc good. Then, or the comparson between the two nvestment regmes, t s natural and nstructve to ocus on the same degree o spllovers between the two nvestment regmes. We should note that allowng the spllover eect gves the benet o savng a varable part o nvestment cost n the non-cooperatve nvestment regme to each o two rms. Furthermore, although a decrease n the degree o spllovers (almost monotoncally) reduces a rm s prot n the non-cooperatve nvestment regme, the qualtatve result regardng the lkelhood o a jont venture s unaected by a change n the degree o spllovers n that regme. A typcal example o ull spllovers n the real busness world s an agreement on a ull-roamng polcy between the dstnct moble provders n the moble communcatons ndustry. 5 For β =, 6 gven rms producton technologes, rm s prots and ts assocated nvestments n the non-cooperatve nvestment equlbrum are derved as ollows. 7 (See Appendx B or rm s prots and nvestments or any β (0, ].) π ncc = π noo = π noc = π nco = k (9k ) (9k 4) (v + c) ef, θ ncc (v + c) = 9k 4 k (9k ) v (9k 4) ef, θ noo = v = θ noo j, 9k 4 (9k ) (3kv (3k ) c) 9k (9k 4) (9k ) (3kv +(3k ) c) 9k (9k 4) ef, θ noc = ef, θ nco = θ ncc j, (3kv (3k ) c), 3k (9k 4) = (3kv +(3k ) c). 3k (9k 4) We should note that gven any combnaton o rms producton technologes, the level o total nvestments n the non-cooperatve nvestment regme s dentcal to that n the 5 See Foros et al. (00). 6 Remember that when β =,bothrms nvestments are strategc complements,.e., θ / θ j > 0. 7 The rst superscrpt "n" represents "non-cooperatve". 7

19 jont venture regme (e.g., when rm chooses an old technology and rm j chooses a new technology, θ oc (= θ co )=(v + c) / (9k 4) = θ noc +θ nco ). Ths ndng mples that wth ull spllovers, each rm chooses the level o nvestment that nternalzes the spllover eect to the other rm n the non-cooperatve nvestment regme Comparson o the two nvestment regmes We now compare the equlbrum prots n the two nvestment regmes. Gven the two rms technology choces, rm s ncentve to undertake a jont venture s obtaned n the ollowng our cases. Case (c, c): When two rms choose a new technology, π cc > < π ncc ef > 4k (v + c) < (9k 4) ef cc. Case (o, o): When two rmschooseanoldtechnology, π oo > < π noo ef > < 4kv (9k 4) ef oo. Case (o, c): When rm chooses an old technology and the rval rm chooses a new technology, π oc > < π noc ef > (3kv (3k ) c)(v + c) < 3(9k 4) ef oc. Case (c, o): When rm chooses a new technology and the rval rm chooses an old technology, 8 In the sem-colluson approach mplemented n the exstng studes, the level o total nvestments n the non-cooperatve nvestment regme concdes wth that n the cooperatve nvestment regme at β =/. The derence between ths result and ours stems rom the ormulaton o cooperaton n the nvestment stage. In the sem-colluson approach, a member rm chooses the nvestment t mplements to maxmze the jont prot o all member rms wth some nvestment technology, whereas under the unanmty cost-sharng rule, a rm proposes total nvestment or the jont-prot maxmzaton wth the same nvestment technologes as n the sem-colluson approach. 8

20 > π co < π nco e F > < (3kv +(3k ) c)(v + c) 3(9k 4) e F co. Usng these results, we obtan the ollowng proposton regardng the lkelhood o a jont venture. Proposton Gven rms producton technologes, a jont venture s most lkely to occur when all rms choose an old technology. By contrast, a jont venture s least lkely to occur when rms technologes are derent. Proo. The statement stems rom the ndng that e F oc < e F oo < e F cc < e F co,whchs obtaned by a drect comparson between any two o the our thresholds. (Insert Fgure.) Accordng to Proposton, the lkelhood that a jont venture wll buld an upstream aclty depends on the rms producton technologes. Fgure llustrates the result o the proposton. (In the gure, the horzontal axs represents the xed cost ef, whlethe vertcal axs represents the xed cost or the adopton o a new technology. Although s rrelevant n the case o exogenous producton technologes, t s a crucal actor or a rm s decson regardng whether t adopts a new technology or not n the later analyss.) As shown n the ollowng paragraphs, the result o the proposton s explaned by three elements: the margnal benet o demand-enhancng nvestment to retal prots, the convexty o the nvestment cost uncton wth respect to the sze o an upstream aclty, and the cost-sharng eect generated n the jont venture regme. Suppose that two rms nvest n the non-cooperatve nvestment regme. Then, each rm s nvestment ncentve depends on the margnal benet o demand-enhancng nvestment to ts retal prot, whch n turn relates to the two rms producton technologes (ther margnal costs). Speccally, the margnal benet o demand-enhancng nvestment 9

21 to rm s retal prots s the lowest (hghest) when rm has an old (a new) technology and the other rm has a new (an old) technology: the orderng o the margnal benet rom lowest to hghest corresponds to the orderng o Case (o, c) to Case (o, o) to Case (c, c) to Case (c, o). As shown above, n the case o ull spllovers, the total nvestment n the non-cooperatve nvestment regme s dentcal to the level o nvestment n the jont venture regme. 9 Then, due to the convexty o (θ), the nvestment cost rm ncurs to buld the upstream aclty n the non-cooperatve nvestment regme, (θ ), s smaller than that n the jont venture regme, s (θ), as long as the total nvestment n the non-cooperatve nvestment regme s dentcal to that n the jont venture regme. Hence, when the xed cost ef s sucently small, the non-cooperatve nvestment regme s preerred to the jont venture regme by each rm, and the magntude o a rm s preerence regardng the non-cooperatve nvestment regme depends on that o the margnal benet o demand-enhancng nvestment to ts retal prots. In contrast, as ef ncreases, the benet o the cost-sharng property n the jont venture regme overcomes the benet nthe non-cooperatve nvestment regme. Thereore, the orderng o the threshold value o ef becomes F eoc < F eoo < F ecc < F eco. From the presumpton that the agreement between the rms s requred to undertake the jont venture, we obtan the result o the proposton. 4 Strategc Technology Choce We now examne two scenaros n whch the rms two knds o nvestment decsons nteract. In ths secton, we examne the scenaro o strategc technology choce. In ths scenaro, each rm non-cooperatvely determnes whether t adopts a new technology or not n the rst stage, antcpatng the opportunty to undertake a jont venture wth the other rm n the second stage. Then, n the second stage, each rm makes a decson 9 Here, the orderng o total nvestment n the non-cooperatve nvestment regme becomes Case (o, o) to Case (o, c)(= Case (c, o)) tocase (c, c). 0

22 regardng whether t agrees to undertake the jont venture, gven the rms producton technologes. The equlbra n the second stage are already shown n Fgure. Accordng to Fgure, we ensure that the ollowng our cases appear based on the nterval o F e. ³ ³ ³ () ef ³0, ef oo, () ef F e oo, ef cc, () ef F e cc, ef co,(v) ef F e co, ef max. 0 Then, n each o the our cases () to (v), we have a technology-choce game n the rst stage by applyng the correspondng prots determned n the second stage. For example, n case (), the prots n the non-cooperatve nvestment regme apply to all combnatons o rms technology choces, because each rm preers the non-cooperatve nvestment regme to the jont venture regme rrespectve o the rms choces regardng producton technology. Smlarly, n case (), the prots n the jont venture regme apply to the stuaton n whch two rms choose an old technology; otherwse, the prots n the noncooperatve nvestment regme apply. Table shows the technology-choce games or all our cases. (Insert Table around here.) We then characterze the equlbrum n a technology-choce game or cases () to (v). The procedure to derve the equlbra s n Appendx C. The equlbra are drawn n Fgure. In the gure, l represents the number o rms that adopt a new technology. (Insert Fgure around here.) We now compare the equlbra wth strategc technology choce and those n the case o exogenous producton technologes. We obtan the ollowng our ndngs rom the comparson. 0 e F max s dened as the level o e F such that a rm s prot can be non-negatve wth the xed cost, rrespectve o ts producton technology and the nvestment regmes.

23 Frst, accordng to Fgure, there s an ntermedate range o n whch only one rm adopts a new technology (l = )nthetechnology-chocegamerrespectveo ex ante symmetrc treatment o rms behavor n our model. As shown n Mlls and Smth (996) and Elbereld (003), such an endogenous rm heterogenety occurs the nvestment technology or the adopton o a new technology s not smoothly convex and rms compete wth quanttes n the retal market (Cournot competton). Under these two presuppostons, there exsts a range o n whch a rm would not lke to adopt a new technology the rval rm adopts a new technology. The reason or ths s that a rm adopts a new technology when ts rval adopts a new technology, that rm s prot can decrease because the equlbrum prce decreases too much due to a large producton expanson. Second, the threshold levels o at whch rms adopt a new technology der between the non-cooperatve nvestment regme and the jont venture regme. In partcular, we nd that a rm s ncentve to adopt a new technology n the non-cooperatve nvestment regme s hgher than that n the jont venture regme. For example, no rm adopts a new technology (l =0) n the non-cooperatve nvestment regme and only > N, whereas n the jont venture regme l =0occurs even or < N. More speccally, when ef >ef co,norm adopts a new technology n the jont venture regme and only ³ >J ef ³< N. Thssduetoacost-sharng eect under the jont venture, whch means that the cost share a rm ncurs ncreases t adopts a new technology whle the other contnues to use an old technology. In act, suppose that s so large that two rms use an old technology. Then, one rm devates to a new technology, that rm must owe a larger cost share o the upstream nvestment under the jont venture. In other words, the cost-sharng eect n the jont venture works negatvely or a new-technology rm. In contrast, the cost-sharng eect does not appear n the non-cooperatve nvestment A dscrete (jump) uncton³ n our analyss satses ths condton. Moreover, the act that J ef s downward slopng toward the rght mples that a rm s ncentve to adopt a new technology decreases as F e becomes large.

24 regme because a rm constantly ncurs a total xed cost ef rrespectve o ts technology choce. Hence, the rm has less ncentve to adopt a new technology n the jont venture regme than t does n the non-cooperatve nvestment regme. 3 Thrd, we ensure that rms technology choces actually aect the lkelhood o a jont h venture to buld an upstream aclty. Speccally, at any ef n the nterval o F e oo, ef cc, whch type o nvestment regme occurs depends on the magntude o. Indeed, when s small ( < N ), both rms adopt a new technology, and the non-cooperatve nvestment regme occurs. The reason s the ollowng: when the xed cost or adoptng a new technology s small, each rm has a strong ncentve to adopt a new technology to obtan the retal-prot eect ampled by spllovers n the non-cooperatve nvestment regme. On the contrary, when s large ( > N ), none o the rms has an ncentve to adopt a new technology. Then, t s better or each rm to enjoy the benet ocost-sharngn the jont venture regme. Interestngly, or h N, N,wend a threshold lne between the jont venture regme and the non-cooperatve nvestment regme (.e., = R ef ). Because only one rm adopts a new technology n the non-cooperatve nvestment regme n ths range o, the retal-prot eect generated by spllovers s small. Then, there s a threshold e F or any above whch the benet o cost sharng n the jont venture regme domnates the retal-prot eect n the non-cooperatve nvestment regme. Fourth, the non-cooperatve nvestment regme dsappears at any ef n the nterval o h ef cc, F eco. I the non-cooperatve nvestment regme occurred n ths range, there would h be only one rm that adopts a new technology, as n the nterval o F e oo, ef cc. However, a larger ef mples the domnance o the benet o cost sharng n the jont venture regme over the retal-prot eect n the non-cooperatve nvestment regme. Hence, only the 3 Note that there s an ndetermnate case such that a rm s ncentve to adopt a new technology n the jont venture regme may be hgher than that n the non-cooperatve nvestment h regme. See ³ the equlbrum n case () n Fgure. In that case, we have multple equlbra or R ef,r ef ; l =0or l =n the jont venture regme. 3

25 h jont venture regme occurs n the nterval o F e cc, ef co.thsndng suggests that when rms can choose ther producton technologes beore they decde whether to undertake ajontventure,thejontventuresmorelkelytooccurthanthecasenwhchther producton technologes are exogenously gven. Because the second and ourth ndngs are undamental and crucal n the scenaro o strategc technology choce, we summarze them as a proposton. Proposton In the scenaro o strategc technology choce, we have the ollowng: () A jont venture deters rms rom adoptng a new technology. () The jont venture regme s more lkely to occur than the case n whch rms technologes are exogenously gven. 5 Strategc Cooperaton Next, we examne the second scenaro,.e., when rms decde whether to undertake a jont venture n antcpaton o each rm s choce o producton technology. Ths scenaro s called strategc cooperaton. As stated n Secton above, each rm s cost share and the level o upstream nvestment are determned based on the rm s producton technology chosen n the second stage. Antcpatng ts rval rm s technology choce and ts own technology, a rm decdes whether t agrees to undertake a jont venture n the rst stage. In Fgure 3, we prepare a benchmark n whch each rm determnes whether t adopts an ecent technology or not by takng an nvestment regme as gven. (Insert Fgure 3 here.) The procedure to derve the equlbra s n Appendx D. Fgure 4 shows the characterzaton o the equlbra. In the gure, l represents the number o rms that adopt a new technology, as n Fgure. 4

26 (Insert Fgure 4 around here.) The characterzaton o the equlbra n the scenaro o strategc cooperaton seems to be qute derent rom those n the case o exogenous producton technologes and n the scenaro o strategc technology choce. We menton the ollowng two ndngs. Frst, as n the scenaro o strategc technology choce, a rm s ncentve to adopt a new technology n the jont venture s weaker than that n the non-cooperatve nvestment regme. Ths s agan due to the cost-sharng eect generated n the jont venture regme. Second, when a rm can decde whether t agrees to undertake a jont venture wth the antcpaton o ts own and a rval s choces o producton technology, the threshold ef betweenthejontventureregmeandthenon-cooperatvenvestmentregmechanges accordngtothexed cost or the adopton o a new technology,. For example, when s n the range o h N, N, the jont venture regme prevalently occurs wth no rm s adopton o a new technology. In act, the non-cooperatve nvestment regme n whch only one rm adopts a new technology s n a small porton when h N, N n Fgure 3. We should note that the prevalence o the jont venture regme occurs even when two rms adopt an ecent technology n the non-cooperatve nvestment regme. ollows. The reason or the prevalence o the jont venture regme n ths range s as When the nvestment cost to adopt an ecent technology s not sucently low, each rm has an ncentve to avod t by takng advantage o the benet ocost sharng n the jont venture regme, because the retal-prot eect generated by spllovers n the non-cooperatve nvestment regme s not sucently large. That s, the costsharng property n the jont venture regme domnates the retal-prot eect n the noncooperatve nvestment regme. Thereore, even at small e F, the jont venture regme s preerred to the non-cooperatve nvestment regme by the two rms. 4 4 In act, one rm adopts a new technology n³ the jont venture regme, the threshold level o F e or the agreement on a jont venture s (/) ef oc + F eco because t relects the nequalty o (/) (π oc + π co ) > < (/) (π noc + π nco ) (see Fgure ). However, because (/) [π oc + π co ] < 5

27 Ths ndng suggests that the undertakng o a jont venture mght be used strategcally by takng advantage o a rm s adopton o a new technology. Thus, the lkelhood o a jont venture does not depend on the magntude o a xed aclty cost when rms have an opportunty to upgrade ther producton technologes. We summarze the above two ndngs as a proposton. Proposton 3 In the scenaro o strategc cooperaton, we have the ollowng: () A jont venture deters rms rom adoptng a new technology. () The jont venture regme s more lkely to occur than the case n whch rms technologes are exogenously gven. 6 Concludng Remarks In ths paper, we have examned the relatonshp between the lkelhood o a jont venture and each rm s decson regardng technology choce by buldng a smple model. In our model, upstream nvestment s assumed to have a demand-enhancng eect, whereas a rm s technology choce has a cost-reducng eect. The man results obtaned rom the analyss are as ollows. Although demand-enhancng nvestment s complementary to costreducng nvestment, a rm s ncentve to adopt an ecent technology becomes weak n the jont venture regme. Ths s due to the cost-sharng eect that s generated under the unanmty cost-sharng rule n the jont venture regme. Then, when the adopton o an ecent technology s used as a strategc devce, a jont venture s more lkely to occur than n the case o exogenous producton technologes (the scenaro o strategc technology choce). In addton, the sze o a xed aclty cost may not matter when a rm has an opportunty to upgrade ts producton technology that mght be ncluded n the contract terms o a jont venture (the scenaro o strategc cooperaton). In partcular, a rm has π oo or h N, N, the threshold that relects (/) (π noc + π nco ) > < π oo moves letward to ³ (/) ef oc + F eco, whch ndcates that the jont venture regme prevalently domnates the noncooperatve nvestment regme n ths range o. 6

28 an ncentve to undertake a jont venture even the xed aclty cost s small, as long as the derence n the number o rms that adopt a new technology s only one between the two nvestment regmes. Two man messages are obtaned rom the analyss n ths paper. Frst, although jont ventures obtan a benet rom avodng the duplcaton o sunk nvestment cost rom a welare vewpont, there s also the dsadvantage o reducng a rm s ncentve to adopt an ecent producton technology. To the best o our knowledge, ths paper s the rst attempt to ormally show ths demert o jont ventures. Second, our analyss ndcates that due to ths weak ncentve to adopt an ecent technology, the lkelhood o a jont venture ncreases when rms have an opportunty to determne ther producton technologes endogenously. As a nal remark, we menton the robustness and lmtaton o the qualtatve results by dscussng several speccatons made n our model. Frst, we have used the unanmty cost-sharng rule to determne each rm s cost share and the nvestment level n the jont venture regme. Even we use a Nash barganng rule n place o the unanmty costsharng rule, the qualtatve property that an ecent rm must ncur a larger cost share o nvestment than an necent rm does not change. Hence, our results also hold under thenashbarganngruleasanalternatvecost-sharngrule. Second, the degree o spllovers aects the derence n the level o upstream nvestment between the jont venture regme and the non-cooperatve nvestment regme. For example, as the degree o spllovers decreases n the non-cooperatve nvestment regme, each rm s producton and prots may decrease n that regme. Then, the jont venture regme s more lkely to occur than t s n the case o ull spllovers. However, the qualtatve result regardng the eect o a rm s endogenous technology choce on the lkelhood o a jont venture stll holds, because the ndng that a rm s ncentve to adopt an ecent technology s weak due to a cost-sharng eect s unaected by the degree o spllovers. 7

29 Fnally, the other actors, such as the number o rms and the product derentaton, certanly aect a rm s retal prot through a change n the erceness o retal competton. Thus, these actors may nluence the lkelhood o a jont venture under any cost-sharng rule. We then need to clary how a rm s endogenous technology choce aects the lkelhood o a jont venture under erce retal competton, whch s a remanng ssue or uture research. Appendx Appendx A: proo o Lemma We prove two ndngs stated n Lemma : the rst s the characterzaton o the unanmty cost-sharng rule wth the assocated nvestment, and the second s to show that the unanmty cost-sharng rule acheves the nvestment that maxmzes the jont prots o all rms. In act, the latter ndng holds regardless o the speccatons o demand and cost unctons wth any gven number o downstream rms. 5 Hence, we show the proo n a general ormulaton o rm prot. Letusdenotetheretalprot oarm by eπ θ(), excludng the shared cost or upstream nvestment. Under the unanmty cost-sharng rule, gven s, rm nds ts nvestment θ () that maxmzes ts prots. In act, the problem o rm s represented by Max θ () π = eπ θ() s F θ (), =,...n. Then, we obtan the rst-order condton as ollows. deπ θ() = s F 0 θ (), =,...n, (3) dθ () 5 Furthermore, ths ndng holds or any type o retal competton regardless o the nterdependency o markets and demand substtutablty. 8